STUDY OF THE INFLUENCE OF INTERACTIVE DRAW UPON DRAWPOINT SPACING IN BLOCK
AND SUBLEVEL CAVING MINES
Adrianus (Adrian) Erwin Halim B.E. (Mining)
M.E. (Mining)
Thesis submitted in fulfillment of the requirements for the Degree of Doctor of Philosophy
Julius Kruttschnitt Mineral Research Centre The University of Queensland
September 2006
I declare that the work presented in this thesis is, to the best of my knowledge and belief, original except as acknowledged in the text. No material has been submitted, either whole or in part, for a degree at this or any other university.
This thesis presents original contributions in the following areas:
• The physical model used in this thesis is a unique and suitable tool to investigate interactive draw and drawpoint spacing in block and sublevel caving mines as it is more closely matches insitu conditions than past models;
• For the first time, with the development of novel instruments, the movement zone could be measured in 3D, albeit only in one axis;
• A more comprehensive quantification of scale distortion between two model scales is provided. Previous work in this area made incorrect conclusion due to the lack of repetition of each model scale experiment;
• A more comprehensive quantification of scale distortion between physical model and full scale is provided. This quantification is better than previous work in this area since it was done at higher height of draw (50m compared to 19m);
• Current theory of interactive draw and drawpoint spacing appears to be not valid for modern block and sublevel caving mines. Previous conclusions were based on the results from a sand model, which has been found to lack similarities with insitu conditions such as an inability to measure extraction zone, unrealistic method of draw, unrealistic friction angle, unrealistic scaled particle size, unrealistic particle shape, and unrealistic stress distribution within the media (i.e.
arching);
• Under ideal draw control when the drawpoints are spaced at a distance less than the width of the isolated extraction zone (IEZ), they do not overlap as thought previously, but just form a plane boundary halfway between them. Under this condition, there is a reduction in geometry of combined extraction zones compared to the superimposed isolated one;
• Confirmation that the extraction and movement zones expand laterally as the draw gets higher, which contradicts most of current theories of gravity flow;
approximately 3m, which is deeper than previously thought (1m);
• The drawpoint widths used by industry currently appears to have no effect upon the width of the extraction zone, which contradicts almost all theories on gravity flow;
• For the first time, a comparison of flow of broken rock in block and sublevel caving is provided;
• The particle size effect upon the width of extraction zone appears to be not as distinct as previously thought;
• The particle size effect appears to take place after 50m height of draw, which means it may be negligible in sublevel caving mines;
• Significant new understandings of the influence of interactive draw upon drawpoint spacing in block and sublevel caving mines.
Adrian Halim
I wish to thank the following people and organisations for their contributions to the completion of this Thesis:
• Mr. Raul Castro, fellow PhD student who worked with me in running the physical model. Without him, the experimental programme would never have be completed;
• Dr. Bob Trueman, my principal supervisor, for his strong support and encouragement;
• Dr. Gideon Chitombo, my associate supervisor, for his practical insights and encouragement;
• The sponsor companies of the International Caving Study II and Mass Mining Technology project (WMC, Newcrest, Northparkes, CODELCO-Chile, LKAB, De Beers, Rio Tinto, BHP-Billiton, Xstrata, INCO, Sandvik-Tamrock, and Orica), who partly funded construction and operation of the physical model;
• The Australian Government, who gave me the APA (Australian Postgraduate Award) scholarship for this thesis;
• Technical officers of JKMRC workshop who constructed the physical models:
Mr Bob Marshall and Mr Mick Kilmartin;
• Mr Jon Worth, senior research assistant in the pilot plant, who helped me dealing with the logistics of the physical model;
• Dr. Geoff Just for his practical advice on physical modelling;
research group: Mr. Italo Onederra, Mr. Ian Brunton, and Mr. Alan Tordoir, to whom I have shared opinions regarding this thesis;
• Finally, I thank my family: Mom, Dad, my brother Anto, and my ex nanny Zus At. Even though you are far away, I know that you always pray for me. Your prayers are my tower of strength to overcome one of the most difficult periods in my life. Without you, I would never have got this great achievement.
- Halim, A., 2004. 3D large scale physical modelling for studying interactive drawing and drawpoint spacing in Block Caving mines, in Proceedings of JKMRC International Student Conference 2004, Brisbane, pp 123-144 (JKMRC, The University of Queensland, Brisbane).
- Two further papers have been submitted for publication to the International Journal of Rock Mechanics and Mining Sciences.
Over the last 10 years, the trend toward the mining of deeper, higher tonnage deposits, and lower grade orebodies have made caving mining methods (Block and Sublevel) increasingly attractive to the global mining industry. This is due to their low mining cost. During this period the scale of these caving operations has increased significantly. Block caves such as Northparkes in New South Wales and Palabora in South Africa, and the Sublevel cave at Ridgeway in New South Wales are examples of this trend.
However, to achieve the low cost of these methods, all aspects must work properly.
Therefore, it is essential to understand all of them to make a proper mine design. One of the key aspects is the gravity flow of broken ore and waste. This controls the amount of the ore recovered in the drawpoints along with the extent to which it is diluted by broken waste rock. The economics of a caving mine depend largely on this aspect. In addition, gravity flow also determines the spacing, and thus the number, of drawpoints required. This dictates the design of extraction horizon, which has a huge impact on capital requirement of the mine.
Despite numerous researches having been carried out, the mechanism of gravity flow of broken ore and waste is still not well understood. In previous studies, numerical modelling has been carried out. However, most of them remain unvalidated. This was due to the unavailability of validation data. The best validation data should come from full scale marker tests. These tests are also the best method to investigate gravity flow of broken rock. However, these tests are tedious, very expensive and only produce site-specific results. Moreover, due to the nature of the mining method these tests so far have only been able to be carried out in Sublevel caving.
Conducting such a test in a block caving mine is still considered not feasible, due to the fact that markers movement will be influenced by caving process, and the cost will be millions of dollars per test. The cost of carrying out such a test in a Sublevel caving mine is approximately $25,000 per test.
In fact, most of the theories about gravity flow have been derived from this kind of modelling, many of which are still being used. However, these theories were derived from sand models, which are considered inappropriate due to the disparity between them and insitu conditions, such as particle size and shape, friction angle, and stress distribution. Therefore, it was decided to use gravel as the model media. Gravel has much closer resemblance to insitu conditions than sand, which makes it ideal as a model media. Even though the dynamic similitude cannot be achieved, evidence from literature suggested that this would not impact the main results of the model, which is the geometry of draw envelopes, as long as the material is cohesionless, the model is large, and geometric similitude is achieved.
As a result, the largest 3D physical model was constructed. This model was able to simulate geometries of current block and sublevel caving mines. Drawpoint spacing in this model could be varied, so its effect upon the gravity flow could be investigated. Also, for the first time, the movement envelope could be measured by extensometer like probes. This has produced a significant improvement in understanding gravity flow.
Results from the physical modelling indicate that current theories used to design extraction horizon may not be accurate since they are largely based on an inappropriate model, i.e. sand model. The sand model has been found to lack similarities with insitu conditions such as an inability to measure extraction zone, unrealistic method of draw, unrealistic friction angle, unrealistic scaled particle size, unrealistic particle shape, and unrealistic stress distribution within the media (i.e.
arching).
The results also produce new findings about the gravity flow such as the fact that extraction zones do not overlap when the drawpoints are spaced at a distance less than the width of Isolated Extraction Zone (IEZ), but just touch and form a plane boundary, reduction of combined extraction zones in the same situation compared with the superimposed isolated ones, the centroid of both extraction and movement zones are deeper than previously thought, the drawpoint widths used by industry
both extraction and movement zones expand as the draw gets higher, the particle size appears not to have a distinct effect upon the width of the extraction zone, the particle size effect appears to be negligible in Sublevel caving mines, and the fact that flow in block caving is comparable with the one in Sublevel caving providing that the material within the blast ring is fully mobilized.
A quantification of scale effect between two model scales is provided. There is no scale distortion between two model scales used in this thesis, 1:30 and 1:100. This quantification is better than previous work in this area, which made incorrect conclusion due to the lack of repetition of each model scale experiment.
A quantification of scale effect between physical model and limited full scale data is provided. It indicates no scale distortion. However, since the full scale test data available is just up to 50m height of draw, more comparisons between model results and full scale trials at a greater height of draw than 50m are needed to confirm scalability for block caving mines.
These results have led to significant new understandings about the influence of interactive draw upon drawpoint spacing in block and sublevel caving mines. The drawpoints must be spaced less than the width of Isolated Movement Zone (IMZ) at height of draw less than the ore column height.
The results also conclude that more physical model experiments, other than described in this thesis, are required. This is due to the fact that due to its size, completing an experiment in this model took a long time, and due to the time and resource limitations, not all experiments considered appropriate for a complete understanding of gravity flow of broken rock could be completed.
STATEMENT OF ORIGINALITY ... ii
ACKNOWLEDGEMENT ... iv
LIST OF PUBLICATIONS ... vi
ABSTRACT ...vii
TABLE OF CONTENTS ... x
LIST OF FIGURES ... xiv
LIST OF TABLES ... xxi
CHAPTER 1 - INTRODUCTION... 1
1.1. BACKGROUND... 1
1.2. RESEARCH OBJECTIVES ... 4
1.3. METHODOLOGY ... 4
1.4. THESIS OUTLINE ... 6
1.5. TERMINOLOGY ... 6
CHAPTER 2 – PREVIOUS RESEARCHES ON GRAVITY FLOW OF BROKEN ROCK IN CAVING MINES ... 9
2.1. MATHEMATICAL MODELS ... 9
2.2. FULL SCALE TESTS ... 12
2.3. PHYSICAL MODELS ... 14
2.3.1. Sand models ... 15
2.3.2. Gravel models ... 28
2.3.3. Similitude ... 31
2.4. CONCLUSIONS ... 35
GUIDELINES USED BY INDUSTRY ... 37
3.1. CURRENT BLOCK CAVING DRAWPOINT SPACING GUIDELINES.. 37
3.2. CURRENT SUBLEVEL CAVING DRAWPOINT SPACING GUIDELINES ... 43
3.2.1. Classical Theory ... 44
3.2.2. “Improved” Theory ... 48
3.3. CONCLUSIONS ... 49
CHAPTER 4 – PHYSICAL MODEL DESIGN ... 51
4.1. DESIGN OF 1:30 SCALE MODEL ... 51
4.1.1. Model features and material handling systems ... 51
4.1.2. Model media ... 60
4.1.3. System of Markers and Movement Probes... 60
4.1.4. Draw rate ... 69
4.2. DESIGN OF 1:100 SCALE MODEL ... 69
4.2.1. Model size ... 69
4.2.2. Drawpoint and feeder size ... 69
4.2.3. Model media ... 70
4.2.4. Resolution of markers and probes ... 70
4.2.5. Draw rate ... 71
4.3. DESIGN OF 1:30 SCALE SLC PHYSICAL MODEL ... 73
4.3.1. Model features ... 73
4.3.2. Material handling system ... 76
4.3.3. Model media ... 76
4.3.4. Marker system ... 76
4.4. CONCLUSIONS ... 79
CHAPTER 5 – PHYSICAL MODEL RESULTS AND ANALYSIS ... 81
5.1. RESULTS OF 1:30 SCALE MODEL ... 81
5.1.1. Experiment 1 Isolated draw ... 82
5.1.2. Experiment 2 Interactive draw from two drawpoints in the same drawbell – 1.2m long drawbell ... 84
drawbell – 1.1m long drawbell ... 86
5.1.4. Experiment 4 Interactive draw from two drawpoints in the same drawbell – 0.5m long drawbell (Teniente 4 South mine geometry) .... 88
5.1.5. Experiment 5 Interactive draw from two drawpoints in the same drawbell – 0.7m long drawbell ... 92
5.1.6. Experiment 6 Interactive draw from four drawpoints – two 0.5m long drawbell, 0.57m separation between drawbells (Teniente 4 South mine geometry) ... 97
5.1.7. Experiment 6 Interactive draw from four drawpoints – two 0.5m long drawbell, 1.06m separation between drawbells ... 101
5.2. RESULTS OF 1:100 SCALE MODEL ... 104
5.2.1. Experiment 1 Isolated draw ... 104
5.2.2. Experiment 2 Repetition of isolated draw and Power’s 7mm ... 107
5.2.2.1. Width of IEZ and IMZ ... 110
5.2.2.2. Effect of drawpoint width upon the width of IEZ ... 112
5.2.2.3. Confirmation of the width of IEZ of 7mm particles ... 113
5.2.2.4. Interaction of extraction zones at higher scaled height of draw ... 114
5.2.3. Experiment 3 Interactive draw from seven drawpoints, 0.74m spacing, interaction between movement zones ... 116
5.2.4. Experiment 4 Interactive draw from 13 drawpoints, 0.48m spacing, interaction between movement zones ... 123
5.2.5. Experiment 5 Interactive draw from 10 drawpoints, 0.48m spacing, interaction between extraction zones ... 125
5.3. DISCUSSIONS ... 130
5.4. RESULTS OF 1:30 SCALE SLC PHYSICAL MODEL ... 133
5.5. CONCLUSIONS ... 136
CHAPTER 6 – SCALABILITY OF PHYSICAL MODEL RESULTS ... 139
6.1. SCALABILITY BETWEEN 1:30 AND 1:100 MODEL ... 139 6.2. SCALABILITY BETWEEN PHYSICAL MODEL AND FULL SCALE . 140
RESULTS ... 145
6.4. SCALABILITY OF THE MOVEMENT ZONES ... 148
6.5. CONCLUSIONS ... 148
CHAPTER 7 – UNDERSTANDING THE INFLUENCE OF INTERACTIVE DRAW UPON DRAWPOINT SPACING ... 149
7.1. CONCLUSIONS ... 163
CHAPTER 8 – CONCLUSIONS AND FUTURE WORKS ... 165
8.1. CONCLUSIONS ... 165
8.2. FUTURE WORKS ... 168
REFERENCES ... 171
APPENDIX A ... 179
APPENDIX B ... 183
APPENDIX C ... 187
Figure 1.1. The draw and movement envelopes (Just 1981) ... 8
Figure 2.1. Kvapil’s model (Kvapil 1965a) ... 15
Figure 2.2. The ellipsoid theory (Kvapil 1992) ... 16
Figure 2.3. Eccentricity values (Janelid and Kvapil 1966) ... 17
Figure 2.4. Laubscher, Heslop and Marano’s model (Marano 1980) ... 21
Figure 2.5. Draw pattern at drawpoint spacing equal to the isolated drawzone width (Heslop 1983) ... 23
Figure 2.6. Reconstructed draw pattern of isolated drawzones at spacing equal to the isolated drawzone width (Heslop 1983) ... 24
Figure 2.7. Draw pattern at experiment of drawpoint spacing of 1.4x the isolated drawzone width (Marano 1980) ... 24
Figure 2.8. Laubscher’s interactive flow theory (Laubscher 2000) ... 25
Figure 2.9. Pressure transmission in coarse material (Kvapil 1965b) ... 27
Figure 2.10. Results of Power’s model (Power 2004) ... 31
Figure 3.1. Laubscher’s drawpoint spacing guideline (Laubscher 1994) ... 37
Figure 3.2. Laubscher’s concept of expansion of interacted drawzones (Laubscher 2000) ... 39
Figure 3.3. Drawpoints with too wide spacing (Richardson 1981) ... 40
Figure 3.4. Drawpoints with too close spacing (Richardson 1981) ... 41
Figure 3.5. Hexagonal drawpoint pattern (Richardson 1981) ... 42
Figure 3.6. Square drawpoint pattern (Richardson 1981) ... 42
Figure 3.7. Classical SLC theory, showing extraction zone geometries ... 45
Figure 3.8. Spacing of sublevel drifts in classical theory, shaded areas are the extraction zones ... 46
Figure 3.9. Explanation of drawpoint spacing in classical theory ... 46
Figure 3.10. Janelid and Kvapil’s front caving concept (Janelid and Kvapil 1966) .. 47
Figure 3.11. Janelid and Kvapil’s front caving sand model (Janelid and Kvapil 1966) ... 48
Figure 4.1. 3D multiple drawpoints physical model ... 53
Figure 4.2. 0.5m long drawbell ... 54
Figure 4.3. 1.2m long drawbell ... 54
Figure 4.4. Two drawbells for four drawpoints experiments ... 55
Figure 4.5. Dumping the material into the hopper ... 56
Figure 4.6. Bucket elevator and loading chute at the top of the model ... 56
Figure 4.7. Vibratory feeders beneath the model ... 57
Figure 4.8. Material flows from drawpoint onto feeder tray ... 58
Figure 4.9. The conveyors and weigh point ... 58
Figure 4.10. Drawing the material at the weigh point ... 59
Figure 4.11. Markers spotted during drawing process ... 59
Figure 4.12. Particle size distribution of model media ... 60
Figure 4.13. An example of markers layout for two drawpoints experiment ... 61
Figure 4.14. An example of markers layout for four drawpoints experiment ... 62
Figure 4.15. Template used to place markers ... 63
Figure 4.16. Movement probes inserted from outside the model ... 64
Figure 4.17. Detail of the movement probe ... 64
Figure 4.18. A movement probe inside the model ... 65
Figure 4.19. A layer of movement probes ... 66
Figure 4.20. Detector box of movement probes, showing that probe no 41 has been triggered ... 66
Figure 4.21. Placement of extraction and movement zone markers ... 67
Figure 4.22. Movement probes testing apparatus ... 68
Figure 4.23. How the movement probe works ... 68
Figure 4.24. Drawpoint with material reeling onto feeder tray ... 71
Figure 4.25. Feeder in 1:100 model... 71
Figure 4.26. An example of markers layout in 1:100 model, from single drawpoint experiment ... 72
Figure 4.27. An example of movement probes layout in 1:100 model, from single drawpoint experiment ... 72
Figure 4.28. Front section of SLC physical model... 74
Figure 4.30. Inside views of SLC physical model ... 75
Figure 4.31. Front wall of SLC physical model ... 77
Figure 4.32. Material handling system in SLC physical model (1) ... 77
Figure 4.33. Material handling system in SLC physical model (2) ... 78
Figure 4.34. An example of markers layout in SLC physical model ... 78
Figure 5.1. IEZ and IMZ at full height of draw for experiment 1, 1:30 model ... 83
Figure 5.2. IEZ and IMZ when IMZ intersected the surface in experiment 1, 1:30 model. Approximately 300 kg of material had been drawn ... 84
Figure 5.3. Extraction and movement zones at full height of draw for two drawpoints drawn interactively in experiment 2, 1:30 model ... 85
Figure 5.4. Extraction and movement zones at full height of draw for two drawpoints drawn interactively in experiment 3, 1:30 model ... 87
Figure 5.5. Plan view at mid height of draw showing each drawpoint extraction zone at full height of draw in experiment 4, 1:30 model ... 88
Figure 5.6. Extraction zones for each drawpoint, looking across the drawbell in experiment 4, 1:30 model ... 89
Figure 5.7. Plan view at mid height of draw showing combined extraction zones with superimposed IEZs at full height of draw in experiment 4, 1:30 model ... 90
Figure 5.8. Section view of combined extraction zones and superimposed IEZs at the same kg material drawn, looking across the drawbell in experiment 4, 1:30 model ... 91
Figure 5.9. Comparison between width of combined extraction zones and superimposed IEZs at various height of draw– 0.5m long drawbell, 1:30 model ... 91
Figure 5.10. Plan view at mid height of draw showing each drawpoint extraction zone at full height of draw in experiment 5, 1:30 model ... 94
Figure 5.11. Extraction zones for each drawpoint, looking across the drawbell in experiment 5, 1:30 model ... 94
with superimposed IEZs at full height of draw in experiment 5, 1:30 model ... 95 Figure 5.13. Comparison between width of combined extraction zones and
superimposed IEZs at various height of draw in experiment 5, 1:30 model ... 95 Figure 5.14. Section view of combined extraction zones and superimposed IEZs at
the same kg material drawn, looking across the drawbell in experiment 5, 1:30 model ... 96 Figure 5.15. Extraction zones of both drawpoints when the movement zones had
“overlapped” and intersected the surface in experiment 5, 1:30 model ... 97 Figure 5.16. Plan view at mid height of draw showing each drawpoint extraction
zone at full height of draw in experiment 6, 1:30 model ... 99 Figure 5.17. Extraction zone of each drawpoint at full height of draw in experiment
6, 1:30 model ... 99 Figure 5.18. Plan view at mid height of draw showing combined extraction zones
with superimposed IEZs at full height of draw in experiment 6, 1:30 model ... 100 Figure 5.19. Comparison between width along the drawbell of combined extraction
zones and superimposed IEZs at various height of draw in experiment 6, 1:30 model ... 100 Figure 5.20. Section view of combined extraction zones and superimposed IEZs at
the same kg material drawn, looking across the centre drawbell in
experiment 6, 1:30 model ... 101 Figure 5.21. Plan view at mid height of draw showing combined extraction and
movement zones at full height of draw in experiment 7, 1:30 model . 102 Figure 5.22. Plan view at mid height of draw showing each drawpoint extraction
zone at full height of draw in experiment 7, 1:30 model ... 103 Figure 5.23. Extraction zone of each drawpoint at full height of draw in experiment
7, 1:30 model ... 103 Figure 5.24. Comparison between normal and undercut drawpoints ... 106 Figure 5.25. Development of IMZ in experiment 1, 1:100 model ... 108
model ... 109
Figure 5.27. Plan view of model floor in experiment 2, 1:100 model ... 110
Figure 5.28. IEZs from experiment 2, 1:100 model ... 111
Figure 5.29. IMZs from experiment 2, 1:100 model ... 112
Figure 5.30. Effect of drawpoint width upon the width of IEZ ... 113
Figure 5.31. Comparison between repetition of 7mm particle size experiment and similar experiment carried out by Power (2004) ... 114
Figure 5.32. Comparison between Power’s particle size effect and the one corrected in experiment 2, 1:100 model ... 115
Figure 5.33. Extraction and movement zones at full height of draw for two drawpoints drawn interactively in experiment 2, 1:100 model ... 116
Figure 5.34. Plan view of model floor in experiment 3, 1:100 model ... 118
Figure 5.35. Movement probes in experiment 3, showing that they passed the IMZs of far west drawpoints, 1:100 model ... 119
Figure 5.36. Movement probes supported above far west drawpoints in experiment 3, 1:100 model ... 121
Figure 5.37. Movement zones of centre drawpoints in experiment 3, 1:100 model, S- N section ... 122
Figure 5.38. Surface profile in experiment 3, 1:100 model ... 122
Figure 5.39. Plan view of experiment 4, 1:100 model ... 123
Figure 5.40. Movement zones at half height of draw in experiment 4, 1:100 model ... 124
Figure 5.41. Movement zones when reached the surface in experiment 4, 1:100 model ... 125
Figure 5.42. Plan view of model floor in experiment 5, 1:100 model ... 126
Figure 5.43. Mid section of extraction zones in experiment 5 at 220 kg material drawn, 1:100 model. Ratio of spacing: 1.1-1.3X the width of IEZ ... 127
Figure 5.44. Section A-A’ in Figure 5.43 ... 128
Figure 5.45. Mid section of extraction zones in experiment 5 at 320 kg material drawn, 1;100 model. Ratio of spacing: 1.0-1.1X the width of IEZ ... 129
Figure 5.46. Section A-A’ in Figure 5.45 ... 130
Figure 5.47. Results of the SLC physical model ... 134
physical model ... 135
Figure 5.49. Comparison between the width of IEZ of block caving and SLC for 20mm particle size ... 136
Figure 6.1. Scalability between 1:30 and 1:100 models ... 140
Figure 6.2. Front section of blast ring at He-Pei mine (Rustan 2000) ... 142
Figure 6.3. Plan view of ring blasting at He-Pei mine (Rustan 2000) ... 143
Figure 6.4. Plan view of the draw body in He-Pei full scale test (Rustan 2000) ... 144
Figure 6.5. An example of plan section of IEZs found in the SLC physical model ... 144
Figure 6.6. Comparison between physical model results and He-Pei test ... 145
Figure 6.7. Scaled IEZ width of 1:100 model results ... 146
Figure 7.1. Ore loss when drawpoints are spaced at the width of IEZ ... 150
Figure 7.2. Development of ore-waste boundary as the draw progress when the drawpoints are spaced at the width of IEZ, showing that uniform drawdown does not occur so early dilution could be expected ... 150
Figure 7.3. Amount of material drawn when markers above drawbell recovered at two drawpoints in 0.5m (15m scaled) drawbell experiments – 1:30 model ... 153
Figure 7.4. Amount of material drawn when markers above drawbell recovered at two drawpoints in 0.7m (21m scaled) drawbell experiment – 1:30 model ... 154
Figure 7.5. An example of extraction zones of 0.5m (15m scaled) drawbell experiment, 1:30 model, showing the ore loss ... 155
Figure 7.6. Extraction zones of 0.7m (21m scaled) drawbell experiment, 1:30 model, showing the ore loss ... 156
Figure 7.7. What will happen if the drawing was continued in the 0.7m (21m scaled) drawbell experiment. It is obvious that the ore loss is reduced but at the same time, some amount of waste is recovered ... 158
Figure 7.8. What happens in a non-ideal draw situation ... 160
drawpoints ... 161 Figure 7.10. Issue in the classical SLC theory ... 163
Table 2.1. Comparison between bN obtained from ellipsoid theory and 3D large scale gravel model ... 19 Table 2.2. Comparison between bN obtained from ellipsoid theory and He-Pei mine
full scale test... 19 Table 2.3. Results of Peters’ model (Peters 1984)... 30
Table 6.1. IEZs from 1:100 scale physical model ... 146
CHAPTER 1
INTRODUCTION
1.1. BACKGROUND
Block caving is a general term that refers to a mass mining method where the extraction of the ore depends largely on the action of gravity. By removing a thin horizontal layer at the mining level of the ore column, which is called undercutting, using standard mining methods, i.e. drill and blast, the vertical support of the ore column above is removed and the ore then caves as a result of the stresses induced around the undercut. As broken ore is removed from the mining level, the ore above continues to break and cave by gravity (Julin 1992). Eventually, the cave reaches the overlying waste or a surface boundary. Block caving is the lowest cost and most productive underground mining method, providing that all aspects are working well.
One of the key aspects of a successful block cave is the control of dilution entry during the drawing of broken ore. The gravity flow of that broken ore controls the amount of valuable material recovered and the extent to which it is diluted by broken waste rock. The amount of ore recovered and waste rock extracted along with it has a huge impact on the economics of mining. In addition, the flow of broken rock also dictates the spacing, and thus, the number of drawpoints required, and the spacing of extraction level drives. The design of the extraction level has a large impact on capital requirements for development of the mine.
Sublevel caving (SLC) is a potentially low cost mining method where the orebody is blasted whilst the mechanically weaker surrounding waste rock collapses naturally as the ore is removed. Operations in the orebody are undertaken in drives developed at relatively small horizontal intervals. Ore is fragmented using blast holes drilled upwards in fans from these headings, allowing the waste rock to cave, then ore is extracted by Load Haul Dumps from the drill drives. As broken ore is extracted at the drawpoint, fragmented ore and enclosing caved waste displace to fill the void.
The principal economic risks to sublevel caving operations are generally acknowledged to be dilution and reduced ore recovery, resulting in effective ore loss.
As in block caving, the gravity flow of broken rock is the main factor influencing these economic risks. It also dictates the spacing of the drawpoints and sublevel intervals both of which have a significant impact upon the capital requirements for developing the mine. Even though SLC is more expensive than block caving, its advantage lays in its ability to be used in any dip of a massive orebody. Block caving is best applied to a vertical or sub-vertical massive orebody such as copper-porphyry and kimberlite pipes. In massive inclined veins such as nickel and magnetite, the application of block caving contains a huge economical risk as significant amount of waste rock may have to be extracted in order to get the whole ore reserve. SLC is usually the most suitable low cost method in this type of orebody, providing that all aspects are working well.
Economic risks and large capital requirements are particularly the case in large, low grade underground mining deposits that are seen by many mining companies as the future replacements for a significant percentage of current low cost large open cut mines. It is these large open cut mines that currently influence the profitability of many mining companies. Caving methods of mining such as block and sublevel caving are widely regarded as the methods of choice for exploiting these deposits by underground methods in the future. Current widely used methods such as Sublevel open stoping, Bench stoping, Long hole stoping and Cut and fill stoping are not as favoured for these deposits due to their generally higher costs.
However, despite the large amount of research that has been carried out in the gravity flow field, 3D simulations of ore recovery and waste rock dilution can still not be done with confidence for conditions in a specific mine (Rustan 2000). As a result of our limited understanding of the mechanism controlling the flow of broken rock, control of crucial dilution and ore recovery factors can be a difficult task. The key is to understanding flow and the quantification of the influence of a large number of factors and their interrelationships.
In previous studies, a number of 2D and 3D mathematical models have been developed (Chen 1997; Gustafsson 1998, Alfaro and Saavedra 2004, Sharrock et al 2004) but these remain largely unvalidated. This was due to the lack of reliable
validating data. The other problems in mathematical modelling are range and time.
Itasca consulting group Inc. in the United States has developed a 3D numerical modelling approach for gravity flow of materials in caving mines based upon the particle flow code PFC3D. However, this package is currently limited to single drawpoint and a 20m draw height due to the large number of particle that need to be simulated. In current block caving mines, the draw height is 150-500m, whereas in SLC, it is 40-50m. Moreover, the simulation of flow into one drawpoint to even a height of 20m can take several days to execute on a fast computer. Even then PFC3D has had difficulties matching draw zone geometries measured in physical models, possibly because of difficulties in modelling the surface roughness of rock particles (Pierce 2005).
All approaches to modelling flow of broken rock in caving mining methods require good calibration and validation data. It would be best to obtain this data from full scale tests (Just et al. 1973; Rustan 2000). However experience has shown full scale tests to be very expensive, extremely time consuming and often the results from these tests have not yielded results that could be used effectively for the development of generally valid modelling approaches (Sandstrom 1972; Just 1981; Gustafsson 1998). There is also a limited ability to change any of the critical parameters that are thought to influence flow of broken rock such as draw height and drawpoint spacing, which limit the ability to quantify their effect.
The difficulties associated with full scale tests have resulted in the extensive use of physical models (e.g. Kvapil 1965a; Janelid and Kvapil 1966; Free 1970; Cullum 1974; Marano 1980; Heslop and Laubscher 1981; Peters 1984). There are problems associated with the use of past physical modelling data to validate and calibrate mathematical models however. Gustafsson (1998) concluded that all shared at least one, and usually several, of the following limitations:
• Controlled, usually fairly narrow, size distribution.
• Two dimensional.
• No account of density differences generated by the blasting process.
• No refilling of the model from the top.
• Unrealistic frictional properties of walls.
• Insufficient markers in the model material.
Gustafsson therefore inferred that physical model tests carried out to date could not be reliably used to validate mathematical models for the prediction of flow characteristics of broken rock. In addition to those limitations, many of them only modelled single drawpoint, which is not suitable for block caving mines application.
Power (2004) used the largest 3D physical model ever constructed to study flow in an attempt to overcome the above limitations. However, he only modelled single drawpoint. In block and sublevel caving, the interaction of extraction and movement zones of neighbouring drawpoints is considered to be the key to extraction level design and the control of dilution and ore loss. The research described in this thesis therefore aims to extend the physical modelling work carried out by Power to drawing from multiple drawpoints, which is termed as interactive draw. This terminology, along with others that are used in this thesis, will be described in detail in Section 1.5. Additionally, Power, as with all previous physical modellers, was only able to measure extraction zones. The development of novel instrumentation as part of this research enabled movement zones to be measured as well. This development has the potential to significantly aid our fundamental understanding of the gravity flow of broken rock.
1.2. RESEARCH OBJECTIVES
The principal objective of this research is to better understand the drawing process of multiple drawpoints in block and sublevel caving mines. This will lead to understanding its influence on determining suitable drawpoint spacing so optimum mine cash flow can be achieved.
1.3. METHODOLOGY
It was found that despite the fact that gravity flow of broken rock in caving mines is still not well understood, several guidelines on determining drawpoint spacing in block caving mines have been published. These guidelines were reviewed and found to contain significant limitations.
Based on a review of the relevant literature, it was concluded that the best way to improve understanding the influence of interactive draw upon drawpoint spacing is by using a large scale 3D physical model. Due to funding constraints Power was not able to study the effects of scale experimentally. Based upon a limited amount of quantitative experimental data found in the open literature, Power concluded that a model scale of at least 1:30 scale would be needed for model results to be scaled to the full scale. However, this model could only simulate a block height up to 100m, which is not as high as modern block caving mines have block height between 150 and 500m. Moreover, this model could not simulate a large draw area typical of a modern block caving mine. Experimental studies were carried out in this research on the effects of scale, enabling model scale to be reduced to 1:100. This in turn enabled some of the limitations with Power’s work to be overcome. This reduced scale model could simulate a block height up to 330m, which is more realistic than the 1:30 scale model, and could accommodate significantly more drawpoints.
Experimental results from multiple drawpoints experiments carried out in the 1:30 scale model contradict current draw theories being used in practice. Experiments carried out at a scale of 1:100 confirmed and extended the findings in the 1:30 model. Based on data collected in these two models, significant understanding on the influence of interactive draw upon drawpoint spacing was gained. This understanding will lead to a better guideline to determine optimum drawpoint spacing, which is one of future works that need to be carried out.
Although most of the model experiments were carried out using a block caving geometry, all the results can be applied to SLC where ore mobilisation is not constrained. This was confirmed by experiments carried out in a 3D SLC physical model at 1:30 scale prior to completing the multiple drawpoints experiments for a block cave geometry. This model was built based on the geometry of Kiruna mine in Sweden. It was initially aimed to further quantify the particle size effect found by Power (2004), the effect of drawing method and back shape upon the width of draw, and to study interactive draw in SLC. However, it was decided then to carry out the latter in a 3D multiple drawpoints block caving model for efficiency. SLC interactive draw theory was in any case derived from the block caving one (Bull and Page
2000), thus the block caving model would meet the requirement to study interactive draw in both methods.
1.4. THESIS OUTLINE
This thesis has 7 chapters, which are as follows:
Chapter 1: Introduction
Chapter 2: Existing methods to simulate gravity flow in caving mines. This chapter reviews all research of gravity flow of broken rock that have been carried out so far, what the drawbacks of these works are, and how these drawbacks will be overcome in research described in this thesis.
Chapter 3: Current drawpoint spacing guidelines used by industry. This chapter reviews all guidelines used by block and sublevel caving mines to determine their drawpoint spacing, and what are the drawbacks of these guidelines.
Chapter 4: Physical model design. This chapter describes the design of both 1:30 and 1:100 scale physical models.
Chapter 5: Physical model results and analysis. This chapter described results and analysis of all experiments carried out in 1:30 and 1:100 scale physical model.
Chapter 6: Scalability of physical model results. This chapter discusses the scalability of the physical model results.
Chapter 7: Understanding influence of interactive draw upon drawpoint spacing.
This chapter described the influence of interactive draw on determining optimum drawpoint spacing.
Chapter 8: Conclusions and further works.
1.5. TERMINOLOGY
In the research of flow of broken rock in caving mines, there are two main concepts describing the shapes formed by material moving within the cave. Various authors have referred to these shapes in different ways.
The first of these is the outline or contour surrounding the original location of material that has been drawn from a drawpoint at any given point in time. This has been defined in various places as the ellipsoid of motion, the ellipsoid of draw, the ellipsoid of extraction, the draw body, the draw area, the draw envelope, or the draw zone. The author will retain the original term as used by each author in the literature review. However, for his own work, the author will use the term Isolated Extraction Zone (IEZ).
The second concept is the outline or contour surrounding the original location of material that has moved from its original location (but not necessarily been removed at the drawpoint) at any given point in time during drawing of a drawpoint. This has been called, amongst other things the limit ellipsoid, the loosening ellipsoid, the ellipsoid of movement, or the movement envelope. Again, the author will retain the original term as used by each author in the literature review. However, for his own work, the term that will be used is Isolated Movement Zone (IMZ). These concepts are shown in Figure 1.1.
The third concept is interaction. Interaction between two or more adjacent drawpoint extraction or movement zones is defined as when these zones expand from their isolated size under the drawing process, as a result of drawing of neighbouring drawpoints.
The fourth concept is overlapping. Isolated extraction or movement zones are defined as overlapped when two or more zones are intersecting each other.
The fifth concept is interactive and isolated draw. Interactive draw is described as when two or more adjacent drawpoints are drawn concurrently. In this research, drawpoints were not drawn simultaneously, but sequentially, in ideal condition, i.e.
the same amount was drawn from a drawpoint, then draw moved to adjacent drawpoint and an equal amount drawn from it, and so on. When only one drawpoint is drawn, it is defined as isolated draw.
Figure 1.1. The draw and movement envelopes (Just 1981)
(IEZ) (IMZ)
CHAPTER 2
PREVIOUS RESEARCHES ON GRAVITY FLOW OF BROKEN ROCK IN CAVING MINES
This chapter reviews and critically examines the works that have been carried out in simulating gravity flow of broken rock in caving mines. It describes why the mechanism of gravity flow is still not well understood despite the large amount of research that has been carried out in the area. At the end of this chapter, the conclusion will outline the best way of improving our understanding of the gravity flow of broken rock in caving mines that will lead to an improved ability to design such mines.
2.1 MATHEMATICAL MODELS
Mathematical models, in the form of computer programs, have been widely used as common engineering design tools. For example, numerical model programs such as MAP3D, FLAC3D and 3DEC are currently commonly used to predict stresses around underground openings. With the sophisticated computer technology available today, it is clear why mathematical models are often a preferred design tool for engineers.
In previous studies, a number of 2D and 3D mathematical models have been developed (eg Chen 1997; Gustafsson 1998; Alfaro and Saavedra 2004, Sharrock et al 2004) using a stochastic or cellular automata approach, but these remains largely unvalidated. For example, Chen attempted to validate and calibrate his stochastic flow model with the results of physical modelling work carried out by Peters (1984).
Peters’ model was the largest physical model built to that time, in a frame approximately 4.5m high by 3.6m wide (Peters, 1984). However this model was essentially 2D (maximum experiment depth < 0.5m) and simulations were carried out using a very narrow range of particle sizes and distributions. Given that the physical properties of the broken material required by Chen’s model were developed
from this physical model, the use of the model to simulate the behaviour of broken material at a mine site is questionable. Nevertheless, Chen’s stochastic model gave very good approximations to the results from the physical model. With modification, improved validation and calibration data, Chen’s model has great promise as it is computationally efficient. Gustafsson attempted to use data from full scale experiments to validate and calibrate his stochastic model. However, the results of these experiments were largely inconclusive. The use of his model in its current form to predict gravity flow of material at a specific site must therefore also be questioned.
Gustaffson’s full scale test will be described in the next sub-section. Sharrock et al (2004) developed CAVE-SIM, which is based on a cellular automata approach. This package has been validated with results from Kvapil’s sand model experiments (Janelid and Kvapil 1966). However, as will be described later in this chapter, sand models have some drawbacks which make this model not suitable to simulate gravity flow of broken rock, such as: an inability to measure the extraction zone; unrealistic particle size, shape and friction angle; and unrealistic stress distribution.
Cundall (Trueman 2004) has begun the development of a 3D numerical modelling approach for gravity flow of materials in the block caving mining method based upon the particle flow code PFC3D. This approach has a possible advantage over the stochastic models in that it attempts to model the physical process of rock interaction. However, the physical process as modelled by PFC3D remains largely unvalidated because of the lack of reliable data from either physical models or full scale tests. Trends and results from the model that contradict current thinking can therefore be challenged. Also, the application of 3D particle flow codes is currently limited to very few drawpoints and extraction heights due to the large number of particle needed. Even the simulation of flow into one drawpoint to a height of extraction of 20m can take several days to execute on a fast computer. Modern block caving extraction heights vary between 140 and 500m. Inclusion of more realistic heights of extraction will further extend computation times and multiple drawpoints need to be modelled to simulate draw at mine scale. Pierce (2005) has noted that the width of extraction zones modelled by particle flow codes is generally less when compared to physical models using gravel as the model media, when using measured
physical properties of the gravel. He has hypothesised that the reason for this may be difficulties associated with modelling surface roughness in particle flow codes.
Another numerical package that is being developed is REBOP (Rapid Emulator Based on PFC3D), (Carlson et al 2004; Pierce 2004, 2005). This model is a response to the difficulties associated with run times in particle flow codes. This model encodes algorithms that describe collapse and erosion during drawing. The input parameters into the algorithms describing erosion and collapse are empirically derived. It was envisaged that PFC3D would be used to produce the necessary empirical data. However, due to the fact that PFC3D cannot practically model sufficient height of draw or number of drawpoints and concerns relating to the modelling of surface roughness, this is not now the case. The empirical data is being derived from the results of the physical model derived both during this study and those of Power (2004). The quantitative understanding of the mechanics of gravity flow being developed as part of this thesis is therefore essential for the development of REBOP.
Other theoretical approaches to the study of the flow in granular materials have idealized it as a continuum (eg Haff 1983; Savage and Hutter 1989; Hwang and Hutter 1995, Verdugo and Ubilla 2004). However, the applicability of using a continuum approach to model granular flow remains debatable. The former three assumed granular materials as a fluid. However, the particles in granular materials are not uniform in size and shape, whereas in fluids, the molecules size and shape are uniform, i.e. spherical. This causes significant difference in contact between particles or molecules which influences stress distribution throughout the media. Kvapil (1965b) stated that pressure transmission in granular materials may take many forms because the grouping of the particles may be random and variegated. This means that Pascal’s law, which states that pressure in a fluid is distributed uniformly to all direction, may not be valid in granular materials.
Verdugo and Ubilla (2004) suggested that since the drawing process of caved rock in a drawpoint is non continuous and only take 6 to 8 tonnes of material, the flow of caved rock are slow and inertial forces acting on it is small and can be neglected.
Thus the whole phenomenon can be considered static and differential equations for static equilibrium of a continuum media are valid. However, Janssen (Hustrulid and Krauland, 2004) found that the full weight of granular materials in a bin is not carried on the bottom of the bin, as the case of solid (continuum) materials. Some of it is transferred as horizontal pressures (arching). This means that the stress distribution in granular materials is different than the one in solid materials.
Nevertheless, when properly validated, mathematical models can be a powerful tool to simulate gravity flow. However, the work of providing reliable validating data must be carried out beforehand. In most of the mathematical models described empirical data to calibrate the models must also be derived. Only particle flow codes are capable of describing flow from first principles and the limitations with this mathematical model have been described. It is then necessary to review the full scale test and physical modelling for this purpose.
2.2 FULL SCALE TESTS
Only five extensive full scale tests to study the flow of granular material in caving mining have been reported in the literature, all for SLC mines rather than block caving: Grangesberg, Sweden (Janelid 1972), He-Pei, China (Chen and Boshkov 1981, Rustan 2000), Kiruna, Sweden (Gustafsson 1998; Quinteiro et al 2001), Ridgeway, Australia (Power 2004), and Perseverance, Australia (Hollins and Tucker 2004). The principle behind these tests was placing individually identifiable markers within experimental production rings in internal fans of marker rings. The coordinates of each marker (X, Y, Z) were recorded and from markers recovered at certain tonnage drawn, the extent of the extraction zone could be plotted at that point.
All full scale tests were carried out for specific geometries and the application of the results to a generalized idealization of flow in block caving mines is not possible.
Full scale tests have never been carried out for a block caving mine, undoubtedly because of the considerable increased cost and difficulty in achieving this relative to an SLC mine for the following reason:
• In current block caving mines, the block or the draw height is more than 150m, which is far beyond the range of available drill machines. Placing markers up to significant block height will be difficult and very expensive;
• Assuming that markers could be placed along the block height, it will take years to complete one test. In sublevel caving, one blasted ring is mucked completely within days, whereas in block caving, one drawpoint is drawn for years. Also, recovering the markers will be a major issue since, with such large geometry, the amount of markers that must be placed will be very large;
• It is likely that movement of markers will be influenced not only by flow, but also by the caving process;
• The cost of such a test will be magnitudes greater than for an SLC geometry. The full scale tests carried out by Power cost approximately $25,000 for a test carried out per blasted ring (Power 2004). The size of the ring was 14m wide, 37m high and 2.6m deep. In a block caving geometry, where the draw column is typically 18m wide, 15m deep and more than 150m high, the cost will be millions of dollars. Moreover, due to possible interaction between drawpoints, it has been suggested that the test must be carried out to cover at least 9 drawpoints, which will make the cost even more expensive.
Alvial (1992) did attempt a partial full scale test in a block caving geometry. He put markers (old tyres) in the extraction level of a mined out sector above Teniente 4 South sector in El Teniente mine, Chile. Within 10 years, 19 markers were recovered in the drawpoints. Since it was only single layer of markers, the markers generally provided only slip information and marker trajectory. Not even site specific flow rules could be developed from the results of the test.
Even if a successful full scale test could be achieved in a block caving environment, results will be insufficient to develop generalized rules because critical parameters such as fragmentation size, drawpoint spacing and block height can not be varied.
Multiple successful full scale trials in different block caving geometries will be required. The likelihood of achieving this in the foreseeable future is remote.
Nevertheless, even limited full scale tests will improve the confidence that we have in model results.
2.3 PHYSICAL MODELS
The use of physical model in caving mines has been carried out for almost a century.
Lehman (1916) and McNicholas et al (1946) used physical model to study the ore recovery in Miami copper mine and Climax Molybdenum mine (both of them are block caving) in the United States. They used crusher ore and waste as the material.
The drawn material was sampled and assayed, and this was used to assess modelling results. They carried out experiments by varying the ore and waste fragmentation, and chute (drawpoint) spacing. However, they only produced qualitative results, i.e.
the effect of chute (drawpoint) spacing to the ore recovery. Since no markers were placed in the model, they did not make any measurements of the drawzones.
However, McNicholas observed that coarse fragmentation yielded larger arches than fine one, thus concluding that coarser material could be drawn at wider drawpoint spacing than the finer one.
In the last forty years, it is the SLC mines that have been using physical modelling extensively for mine design purposes. Redaelli (1963) appears to be the first person to have used physical modelling for designing an SLC mine. He used this model results to determine ring blasting pattern and mine layout in Koskullskulle mine in Sweden. The most notable physical modelling work is that carried out by Janelid and Kvapil (1966). The results of this work have significantly influenced SLC mine design. This work will be described in detail later in this section. Other works include Airey (1965), Free (1970), Sandstrom (1972), Cullum (1974), McMurray (1976), Sarin (1981), and Stazhevskii (1996). However, these works were not as detailed as Janelid and Kvapil’s. In fact, most of them referred thoroughly to Janelid and Kvapil.
To date, there have been two kinds of physical model based on the material used:
sand and gravel models. Early physical modellers used sand as the material due to the easiness in handling and the reduced overall scale of the model. From these models, concepts of gravity flow of broken material in caving mines were initiated.
Many block and sublevel caving mines use the theories proposed by Laubscher (1994, 2000) and Janelid and Kvapil (1966) which are mainly predicated upon the results of sand models.
2.3.1. Sand models
Kvapil (1965a, 1982, 1992) appeared to be the first person to attempt a quantitative approach for the gravity flow of broken rock. His first work aimed to provide mathematical relationships relating to the flow of granular material in hopper and bins. Shortly afterwards with Janelid (Janelid and Kvapil 1966) he extended this work into idealizing gravity flow for large scale iron ore mines in Sweden, which used SLC as their mining method. Although just using small scale 2D models initially, his work proved to be significant and was used as a design tool for many years.
Kvapil constructed a simple vertical glass model (bin) with layered white and black sand filling. The model had a slot in its bottom. When the slot was opened, the sand flowed out in phases shown in Figure 2.1. It can be seen that only a certain part of the whole material in the bin started moving at the time the slot was opened.
Figure 2.1. Kvapil’s model (Kvapil 1965a)
Based on observation in this model, it was postulated that the material that had been discharged after a given period of time originated from within an approximately ellipsoidal zone, which Janelid and Kvapil (1966) termed the ellipsoid of motion, draw or extraction. Beside it, there is another zone which they termed the limit or loosening ellipsoid. Material between the ellipsoid of extraction and a corresponding ellipsoid of loosening was loosened and displaced but did not reach the discharge point (the slot). The material outside the ellipsoid of loosening remained stationary.
As draw proceeded, an originally horizontal line drawn through the material deflected downwards in the shape of an inverted cone. The shape of this draw cone indicated how the largest displacements occur in a central flow channel. This theory is shown in Figure 2.2.
Figure 2.2. The ellipsoid theory (Kvapil 1992)
The shape of a given ellipsoid of extraction can be described by its eccentricity
(
2 2)
121
N N N
b
a a −
ε =
where aN and bN are the major and minor semi-axes of the ellipsoid of extraction as shown in Figure 2.2. The ellipsoid shape and size is determined by particle size of
the flowing material at the same discharge opening width and the height to which the material is drawn. Small particles were found to have greater eccentricity than the larger ones, and thus had a slimmer and more elongated shape. The eccentricity increases with increased height of draw. In other word, the shape and size of the ellipsoid expands with increased height of draw.
It was assumed that the horizontal cross section of the ellipsoid is circular. In practice, ε varies between 0.90 and 0.98 depending on the draw height as shown in Figure 2.3. It is considered that the range of 0.92 to 0.96 is the most common, at least for SLC mines.
Figure 2.3. Eccentricity values (Janelid and Kvapil, 1966)
With the larger draw heights in block caving, eccentricities greater than 0.96 may be more appropriate even though fragmentation tends to be coarser than in SLC mines.
Since aN is half the draw height, bN then could be calculated using the equation above. Janelid and Kvapil thus developed the design criteria of SLC mines based on this ellipsoid concept, such as location of sublevel drifts, ring burden, and the optimum width of the drawpoint drift relative to the fragmentation size of the broken ore.
There is another method to calculate bN (Janelid and Kvapil 1966). If the volume of discharged material, VN, and ellipsoid height, hN is known, then bN could be calculated using equation:
=
N N
N h
b V
094 . 2
h (m)
ε
Regarding the ellipsoid of loosening, Janelid and Kvapil provided relationships as follows. It was assumed that the ellipsoid of loosening has the same shape, thus eccentricity, with the ellipsoid of extraction. The material between two ellipsoids will loosen and displace but will not report to the discharge point. This loosening is described by the loosening factor ά as
N G
G
E E
E
= − α
where EG is the volume of the ellipsoid of loosening and EN is the volume of the ellipsoid of extraction. The value of α varies from 1.066 to 1.100. Janelid and Kvapil stated that in most granular materials, α tends towards the lower figure of 1.066. If we apply this figure to equation above, we obtain
N
G E
E ≈15
This means that the volume of the ellipsoid of loosening is about 15 times greater than the volume of the ellipsoid of extraction. Thus the height of ellipsoid of loosening hG could be approximated as
N
G h
h ≈2.5
Kvapil’s ellipsoid theory since then has been widely accepted as a design guideline in sublevel caving mines around the world. However, some subsequent sand modellers found that this theory does not model the flow accurately (Heslop 1983;
Heslop and Laubscher 1981; Laubscher 1994, 2000; Marano 1980; McCormick 1968). McCormick found that the shape of the body of motion resembles a cylinder with cone shape at the base. Marano, Heslop and Laubscher (1980, 1981, 1983, 1994, 2000) also observed a similar thing in their sand model. Their model will be discussed in detail later in this sub-section.
The author made comparison between the values of bN calculated using the chart shown in Figure 2.3 and the result of the 3D large scale gravel model experiments carried out by Power (2004) and the author of this thesis, as shown in Table 2.1. The gravel models will be discussed in the next section.
Table 2.1. Comparison between bN obtained from ellipsoid theory and 3D large scale gravel model
Case hN (m) aN (m) ε bN (m) bN from gravel model (m) Modern Kiruna SLC
Ridgeway SLC Block caving (P50 7mm) Block caving (P50 20mm)
47.5 37 99 102
23.75 18.5 49.5 51
0.988 0.983 0.99 0.99
3.7 3.4 7.0 7.2
6 5.4 12.15
13.5
A comparison was also made with the results of the full scale test carried out at He- Pei mine in China (Chen and Boshkov 1981, Rustan 2000) as shown in Table 2.2.
This full scale test will be described in detail in Section 2.3.3 and Chapter 6.
Table 2.2. Comparison between bN obtained from ellipsoid theory and He-Pei mine full scale test
hN (m) aN (m) ε bN (m) bN from full scale test (m) 18
27 34
9 13.5
17
0.977 0.980 0.982
1.9 2.7 3.2
3.0 5.0 6.1
The discrepancies between values obtained from ellipsoid theory with the gravel model and full scale test suggest that the sand model is not suitable to simulate gravity flow in caving mines.
In spite of that, many mining textbooks today still contain this theory (e.g. Brady and Brown 1993; Brown 2002; Hartman 1987). This demonstrates the general acceptance of the ellipsoid theory.
It is interesting to note that since Kvapil published his ellipsoid theory, no one ever tried to apply this theory to block caving mines until the 1980’s. Kvapil himself carried out some experiments in multiple discharge openings hoppers (Kvapil 1965a). He concluded that to ensure good hopper activity, the distance between openings should be less or equal than the width of mobile flow, or the width of the
ellipsoid of extraction. With this arrangement, the formation of passive zones between openings will be limited to a minimum. This is probably the first concept of interactive draw. However, no one carried out further research in the area of interactive draw until Marano, Heslop and Laubscher did it in the early 1980’s for block caving.
In the late 1980’s when working as a consultant at El Teniente mine, Kvapil extended his ellipsoid theory to determine drawpoint spacing (Flores 1993, 2004). He proposed an equation to calculate the spacing (S):
a
N w
b S = 2 +
wa is the effective drawpoint width, i.e. the loading width of broken ore in the drawpoint. It was assumed that wa is approximately 75% the drawpoint width (Flores 1993). From this equation, it is clear that the spacing should be at least equal to the width of the ellipsoid of extraction.
However, in his paper about SLC design, Kvapil proposed that the drawpoint spacing must be less or equal to the width of ellipsoid of loosening (Janelid and Kvapil 1966, Kvapil 1982, 1992). Since the ellipsoids of extraction do not touch, for many years Janelid and Kvapil’s SLC design had been regarded as an isolated draw case. Janelid and Kvapil never explained why the spacing of the drawpoints is based on the width of ellipsoid of loosening. The author managed to provide the most logical explanation of this, which will be described in the next chapter.
In term of interactive draw in SLC, Bull and Page (2000) were the first to propose this concept widely. Their concept is based on Laubscher’s block caving drawpoint interaction theory, which will be described later in this sub-section. This concept will be described in more detail in the next chapter.
Kvapil’s ellipsoid theory was challenged by Laubscher, Heslop and Marano (Heslop 1983; Heslop and Laubscher 1981; Laubscher 1994, 2000; Marano 1980). They carried out experiments in a 3D sand model, which was specifically built to investigate the interactive drawing of adjacent drawpoints. The model consisted of a metal box with a size of 760mm long x 760mm wide x 2400mm high. The base
contained 50 holes, evenly spaced, with a diameter of 25mm, representing the drawpoints. The spacing between each hole was 108mm, but could be varied for different experimental conditions by closing some of the drawpoints. In order to simulate the actual condition in mines, a modelled crown (major apex) pillar, made of polystyrene foam, was place above the drawpoints. Figure 2.4 shows the model.
Figure 2.4. Laubscher, Heslop and Marano’s model (Marano 1980)
The scale of the model was 1:80. This represented the ore block of 60m long x 60m wide, with 2m drawpoint width. The block height could be varied by filling the model to the top or only part of it. When full to the top, it would simulate a block height of 192m at the scale used. The material used was mostly river sand, with median size (P50) of 0.7mm. In some experiments, the river sand was mixed with pit sand, creating a median size of 0.6mm. The friction angle of the material was measured to be 37º, which was significantly less than insitu broken rock which generally have friction angles of about 45º (Janelid 1972). The drawing followed the practise used in slusher system, i.e. a row of drawpoints was drawn simultaneously then moved to the next row and so on.
To monitor the movement of the material under draw, coloured layers of sand were used. This was done by mixing the river sand with a powder pigment and adding a little cement to fix the colour of the sand. The coloured horizontal layers were placed at regular intervals in the sand. A total of six layers were used, spaced 150mm apart and 30mm thick each. At completion of the experiments, water was poured on top of the sand in the model, in order to wet it thoroughly. When watering, all drawpoints were closed using ordinary masking tape, to avoid any loss of sand. Draining the water was allowed for by making small holes in the masking tape. It was found that the wet sand had enough cohesion to permit the cutting of vertical sections through the material and allowing the observation of the position of the coloured layers by means of detailed sketches, as shown in Figure 2.5, 2.6 and 2.7. It was claimed that a high degree of accuracy was obtained. Also the watering technique was claimed to be very practical and work very well. Some compaction was observed, resulting in a small overall lowering of the layers, but this was considered negligible.
Laubscher, Heslop and Marano (1980, 1981, 1983, 1994, 2000) carried out experiment in which the drawpoints were spaced at the width of the isolated drawzone (IDZ), which was measured to be 108mm from previous experiment. They found that uniform lowering of the upper markers occurred as shown in Figure 2.5.
They then compared this result with the reconstructed drawzone of isolated drawpoint experiment carried out previously at the same drawpoint spacing as shown in Figure 2.6. From this comparison they then concluded that the ellipsoid theory does not apply in this situation, which later they termed as interactive flow theory.
They also carried out several experiments in which the drawpoints were spaced at 1.4 times the width of IDZ, as shown in Figure 2.7. There was uniform drawdown, as observed in previous experiment when the drawpoints were spaced at the width of the IDZ, as shown in Figure 2.5.
From this experiment, Laubscher then proposed his drawpoints interaction theory.
He stated that, based on the model experiments and interpretation of stresses around underground excavations, interaction will occur when the drawpoints are spaced no more than 1.5 times the width of the IDZ (Laubscher 1994, 2000). This means that
